The Carter administration says it now sees hope for significant improvement in American-Soviet relations resulting from an expected agreement on a new nuclear arms pact and combined efforts to help produce an Arab-Israeli peace settlement.

If the present pattern of moderation between Moscow and Washington can be sustained, senior administration officials are envisioning spreading American-Soviet co-operation in zones of high tension.

That "if" however, is an overriding qualification. Even so, the expectations now being raised are a striking turnabout from the very cold start last winter between the Carter administration and the Soviet Union. Moreover, the prospects now being raised surpass mere atmospherics.

A very tenuous start toward mutual accommodation of interests has been made in grappling with the volatile Rhodesian black-white struggle. The Soviet Union, at black African urging, abstained in the United Nations Security Council from blocking the take-off of the British-American attempt to produce a cease-fire in the Rhodesian guerrilla war.

The United States and the Soviet Union also may both now work through the Organization of African Unity to help cool down the crisis in the Horn of Africa. There the Soviet Union is straddling warfare between two of its military clients, Ethiopia and Somalia, and the United States shares an interest in curbing the conflict.

At the core of the American-Soviet relationship, of controlling factor is the outcome of the current negiotiations in the nuclear strategic arms limitation talks (SALT).

This, in turn, makes the U.S. Senate, which holds ultimate power over authorizing a SALT treaty, almost as much of a bargaining partner for the Carter administration as the Russians in setting the basic condition of American-Soviet relations. However, as Secretary of State Cyrus R. Vance's encounter Friday with potential SALT opponents demonstrated, the administration faces a skeptical audience for convincing the required two-thirds of the Senate that its views about Soviet intentions are justified.

In separate interviews, Friday and yesterday, President Carter and Vance both sought to convince the skeptics that prospects are good for American benefit in the SALT negotiations, and also in U.S.-Soviet cooperation to produce a Middle East peace settlement.

"Lately, I have been encouraged" by the outlook for American-Soviet cooperation, the President told a group of news editors in an interview Friday that was released for publication yesterday.

In the SALT negotiations, he said. "I think we are approaching a settlement with the Soviets, if they continue to act in as constructive a fashion as they have exhibited in the last few weeks."

Also, he said, "we have been able to get the Soviets, for the first time, to take a moderate position on the Middle East."

Although the American-Soviet "guidelines" for an Arab-Israeli settlement that were published Oct. 1 aroused Israeli indignation. Carter described the statement as "very constructive." He said "we are making slow, tedious progress toward a Geneva conference" on the Middle East.

Carter repeated, however, that "I don't favor and have never favored an independent Palestinian state in the West Bank" of the Jordan River or elsewhere in Israeli-occupied territory.

He spoke hopefully, however of the prospect for discussing "the future status of the West Bank, the Gaza strip" among "the Palestinians, Jordan, Egypt and Israel" even though there continues to be "a serious question about Palestinian representation" in the talks.

Vance, in an interview with The Washington Post in his office yesterday, said he plans to meet Monday with Soviet Ambassador Anatolly F. Dobrynin on a range of issues.

In their Oct. 1 statement, the United States and the Soviet Union pledged "through joint efforts and in their contacts with the parties concerned to facilitate in every way the resumption of the work of the [Geneva] conference not later than December 1977."

Arab sources are now reporting the projected date of the conference as Dec. 21 or 22. American sources agree that is the intended time frame, but with many obstacles yet to be surmounted to pin it down, notably, the insistence of the Palestine Liberation Organization to the represented and Israel's adamant objection to that.

According to Arab sources, the diplomatic barrier over inviting the PLO is intended to be circumvented by extending an invitation to the Arab League. The Arab League, in turn, would invite to the conference Egypt, Jordon, Syria, Lebanon and Palestinians that Israel hopefully would accept, in the context of a single Arab delegation, without an invitation going to the PLO as such.

The United States is counting on the Soviet Union to help induce the PLO, and also Syria, to go along with the overall conference plan. None of the Arab nations has yet responded officially to the American-Israeli "working paper" for reconvening the conference.

Vance, in the interview, declined to comment on what he intends to discuss with Dobrynin.

The Carter administration officially has rejected the strategy of "linking" all major American-Soviet issues, adovated by former Secretary of State Henry A. Kissinger. Nevertheless, Vance said that "if progress is being made in SALT, that tends to affect the total relationship" with the Soviet Union.

In the SALT negotiations, Vance said, the Carter administration now sees the prospect for a significant advance in banning "the testing and deployment of new weapons systems," in addition to lowering arms ceilings.

The ban on new nuclear arms system would be "a very important step forward," he said, beyond the goals projected by former President Ford and Soviet leader Leonid I. Brezhnev at Vladivostock in 1974.

Vance also said that the American-Soviet declaration two weeks ago on joint guidelines for an Arab-Israeli settlement "was very carefully thought out."

"It was not something that was lightly done," he said.

Vance said he gave "a great deal of thought" to the idea of bringing the Soviet Union into the negotiations on the Middle East, during and after his trip there in August. That trip [WORD ILLEGIBLE] to overcome the barriers to launching new Geneva talks, especially the obstacle over how to deal with the question of Palestinian representation and the PLO.

After discussing the matter with the President and getting his approval, Vance said, he raised the idea of a point declaration with the Soviet Union and received "a positive initial response." Draft language was exchanged, resulting in the statement issued jointly by Vance and Soviet Foreign Minister Andrei A. Gromyko at the end of Gromyko's talks last month with Carter and Vance.

The statement came under sharp criticism, especially from Israel and its supporters. It was attacked on grounds that it prematurely brought the Soviet Union back into the center of Arab Israeli diplomacy, after years of American effort to minimize the Soviet role.The Carter administration defended its coordination with the Soviet Union as an important advance toward reconvening the Geneva conference for which they are co-chairman.

It is the premise of the Carter administration's strategy that the Soviet Union shares an interest in a settlement of the interminable Arab-Israeli conflict, to eliminate the risk that a new war can spread to involve the two superpowers. Even if that premise proves wrong. Carter strategist contend, there is no cost to the United States in testing it.